Influence of Dimensionality on Thermoelectric Device Performance

TL;DR

This paper uses the Landauer formalism to analyze how the dimensionality of thermoelectric devices affects their performance, highlighting the importance of channel utilization, density, and engineering the transmission function.

Contribution

It provides a comparative analysis of thermoelectric coefficients across different dimensions and explores the potential performance improvements through engineering the transmission function M(E).

Findings

Lower dimensions can utilize channels more effectively.

High packing density is necessary for lower-dimensional advantages.

Engineering M(E) into a delta-function can improve performance by ~50%.

Abstract

The role of dimensionality on the electronic performance of thermoelectric devices is clarified using the Landauer formalism, which shows that the thermoelectric coefficients are related to the transmission, T(E), and how the conducing channels, M(E), are distributed in energy. The Landauer formalism applies from the ballistic to diffusive limits and provides a clear way to compare performance in different dimensions. It also provides a physical interpretation of the "transport distribution," a quantity that arises in the Boltzmann transport equation approach. Quantitative comparison of thermoelectric coefficients in one, two, and three dimension shows that the channels may be utilized more effectively in lower-dimensions. To realize the advantage of lower dimensionality, however, the packing density must be very high, so the thicknesses of the quantum wells or wires must be small. The potential benefits of engineering M(E) into a delta-function are also investigated. When compared to a bulk semiconductor, we find the potential for ~50 % improvement in performance. The shape of M(E) improves as dimensionality decreases, but lower dimensionality itself does not guarantee better performance because it is controlled by both the shape and the magnitude of M(E). The benefits of engineering the shape of M(E) appear to be modest, but approaches to increase the magnitude of M(E) could pay large dividends.